• Communications of Mathematical Education
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• v.25 no.1
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• pp.147-166
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• 2011

In this paper, we listed and discussed the properties of the Pythagorean triples which 5 gifted 9th graders could draw in spreadsheets environments. And we also discussed their implications. In detail, in spreadsheets environments students could make the table of Pythagorean triples easily under several conditions of generate numbers of Pythagorean triples. And they could draw several properties of Pythagorean triples from the tables and could prove them. In spreadsheets environments it is easy to give students chances of generalization of the properties of Pythagorean triples which they had obtained from the concrete table of Pythagorean triples.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.45-60
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• 2009

In this paper, we investigate homomorphisms in proper $JCQ^*$-triples and derivations on proper $JCQ^*$-triples associated to the following Pexiderized functional equation $$f(x+y+z)=f_0(x)+f_1(y)+f_2(z)$$. This is applied to investigate homomorphisms and derivations in proper $JCQ^*$-triples.

• Journal of KIISE
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• v.41 no.10
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• pp.762-773
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• 2014

As the web of data is increasingly producing large RDFS datasets, it becomes essential in building scalable reasoning engines over large triples. There have been many researches used expensive distributed framework, such as Hadoop, to reason over large RDFS triples. However, in many cases we are required to handle millions of triples. In such cases, it is not necessary to deploy expensive distributed systems because logic program based reasoners in a single machine can produce similar reasoning performances with that of distributed reasoner using Hadoop. In this paper, we propose a scalable RDFS reasoner using logical programming methods in a single machine and compare our empirical results with that of distributed systems. We show that our logic programming based reasoner using a single machine performs as similar as expensive distributed reasoner does up to 200 million RDFS triples. In addition, we designed a meta data structure by decomposing the ontology triples into separate sectors. Instead of loading all the triples into a single model, we selected an appropriate subset of the triples for each ontology reasoning rule. Unification makes it easy to handle conjunctive queries for RDFS schema reasoning, therefore, we have designed and implemented RDFS axioms using logic programming unifications and efficient conjunctive query handling mechanisms. The throughputs of our approach reached to 166K Triples/sec over LUBM1500 with 200 million triples. It is comparable to that of WebPIE, distributed reasoner using Hadoop and Map Reduce, which performs 185K Triples/sec. We show that it is unnecessary to use the distributed system up to 200 million triples and the performance of logic programming based reasoner in a single machine becomes comparable with that of expensive distributed reasoner which employs Hadoop framework.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.1
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• pp.27-36
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• 2006

In [1], the concept of generalized (${\theta}$, ${\phi}$)-derivations on rings was introduced. We introduce the concept of linear ${\theta}$-derivations on $JB^*$-triples, and prove the Cauchy-Rassias stability of linear ${\theta}$-derivations on $JB^*$-triples.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1109-1118
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• 2019

In this paper, we introduce the notion of residuated and Galois connections on adjoint triples and investigate their properties. Using the properties of residuated and Galois connections, we solve fuzzy relation equations and give their examples.

• Korean Journal of Mathematics
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• v.21 no.3
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• pp.351-363
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• 2013

We study the properties of weak extended order algebras having adjoint pairs (triples) or Galois pairs. In particular, we investigate the various laws on weak extended order algebras.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.215-223
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• 2003

Parks [7] showed that there is an one to one correspondence between good pairs of subgroups in G and irreducible monomial characters of G. This provides a useful criterion for a group to be monomial. In this paper, we study relative monomial groups by defining triples in G, and find relationships between the triples and irreducible relative monomial characters.

• Proceedings of the Korean Society of Computer Information Conference
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• 2009.01a
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• pp.411-416
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• 2009

웹 온톨로지 언어의 개발에 따라 웹 온톨롤지를 저장하기 위한 다양한 저장소들이 개발되었으며 이러한 웹 저장소는 관계형 데이터베이스 모델을 기반으로 하고 있다. 또한 웹 온톨로지 데이터를 검색하기 위한 질의 언어로서 W3C에서 SPARQL을 제안하였다. 웹 온톨로지 저장소로서 관계형 데이터베이스가 활발히 개발되고 SPARQL의 이용이 증가함에 따라 SPARQL을 SQL로 변환 하는 알고리즘의 필요성이 대두되었다. 지금까지 제안된 변환 알고리즘들은 SPARQL-to-SQL 변환 알고리즘이 저장소 구조에 종속적이라는 문제점이 있다. 이를 해결하기 위하여 관계형 뷰를 기반으로 저장소에 독립적인 변환 알고리즘을 활용할 수 있는 모델이 제안되었다. 그러나 제안된 모델에서 변환 알고리즘을 독립적으로 활용하기 위해서는 사전에 사용자가 SQL 문을 작성하여 수동적으로 뷰를 생성해 주어야 한다. 이 경우 수동적인 SQL 작성으로 인한 불편함과 사용자의 실수로 인한 SQL문의 오류가 생길 수 있다는 문제점이 있다. 따라서 이 논문에서는 이러한 문제점을 해결하기 위하여 다양한 웹 온톨로지 저장소 모델 OWL 관련 시스템 개발에 가장 많이 사용되고 있는 Jena 저장소를 이용하여 독립적 저장소 활용을 위한 뷰 생성 독인 Jena-to-TRIPLES 변환 도구를 제안한다.

• Journal of Internet Computing and Services
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• v.7 no.2
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• pp.9-21
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• 2006

Researches on enhancing the searching function of the web service using the ontology concept have been studying. One of them suggests a searching method for UDDI using DAML and DAML+OIL. However this approach has inconveniences to use operations proper to the circumstance and to define respective ontologies according to them. To solve these problems, we introduce an effective method of dealing with N-Triple, filtering care Triples, merging Triples, semantic connection between Triples and searching Triples for searching information and recommending the results in semantic web environment. Furthermore, we implement this proposed method in a system to test it. Finally, we test the system in the virtual semantic web environment for out research analysis.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2021.10a
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• pp.236-239
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• 2021

With the growth of AI technology, the scale of Knowledge Graphs continues to be expanded. Knowledge Graphs are mainly expressed as RDF representations that consist of connected triples. Many RDF storages compress and transform RDF triples into the condensed IDs. However, if we try to transform a large scale of RDF triples, it occurs the high processing time and memory overhead because it needs to search the large ID mapping table. In this paper, we propose the method of converting RDF triples using Hash-based ID mapping tables with MapReduce, which is the software framework with a parallel, distributed algorithm. Our proposed method not only transforms RDF triples into Integer-based IDs, but also improves the conversion speed and memory overhead. As a result of our experiment with the proposed method for LUBM, the size of the dataset is reduced by about 3.8 times and the conversion time was spent about 106 seconds.